This invention is in the field of audio amplifiers, and is more specifically directed to pulse-width modulated class D audio power amplifiers.
As is fundamental in the art, electronic amplifier circuits are often classified in various “classes”. For example, the output drive transistors of class A amplifier circuits conduct DC current even with no audio signal, and the entire output voltage swing is of a single polarity. A class B amplifier, on the other hand, typically includes complementary output drive transistors, driving an output voltage swing including both positive and negative polarity excursions. Class B amplifiers are necessarily more efficient, because both complementary output drive transistors are never on at the same time. Class AB amplifiers maintain a small bias current through complementary output drive transistors, so that the output voltage swing is centered slightly above (or below) ground voltage. While the non-zero bias current renders class AB amplifiers theoretically less efficient than class B amplifiers, class AB amplifiers avoid the crossover distortion of class B amplifiers.
In recent years, digital signal processing techniques have become prevalent in many electronic systems. The fidelity provided by digital techniques has increased dramatically with the switching speed of digital circuits. In audio applications, the switching rates of modem digital signal processing are sufficiently fast that digital techniques have become accepted for audio electronic applications, even by many of the fussiest “audiophiles”.
Digital techniques for audio signal processing now extend to the driving of the audio output amplifiers. A new class of amplifier circuits has now become popular in many audio applications, namely “class D” amplifiers. Class D amplifiers drive a complementary output signal that is digital in nature, with the output voltage swinging fully from “rail-to-rail” at a duty cycle that varies with the audio information. Complementary metal-oxide-semiconductor (CMOS) output drive transistors are thus suitable for class D amplifiers, as such devices are capable of high, full-rail, switching rates such as desired for digital applications. As known in the art, CMOS drivers conduct extremely low DC current, and their resulting efficiency is especially beneficial in portable and automotive audio applications, and also small form factor systems such as flat-panel LCD or plasma televisions. In addition, the ability to realize the audio output amplifier in CMOS enables integration of an audio output amplifier with other circuitry in the audio system, further improving efficiency and also reducing manufacturing cost of the system. This integration also provides performance benefits resulting from close device matching between the output devices and the upstream circuits, and from reduced signal attenuation.
In addition to audio amplifiers, class D amplifiers are also now used in other applications. Modern switching power supplies utilize class D power amplifier techniques. Class D amplifiers are also used in some motor control applications, such as voice coil motors for positioning the read/write heads in modem computer disk drives.
By way of background, FIG. 1 illustrates a basic conventional natural sampling pulse width modulator 1, in an open-loop mode, as used to generate a pulse width modulated (PWM) output signal. As shown in FIG. 1, conventional pulse width modulator 1 includes comparator 5, which compares an input signal x(t) at its positive input with a unity amplitude triangle wave, generated by signal source 3 and appearing at its negative input, to produce a two-level PWM output signal p(t). The triangle waveform is at a period T and a switching frequency Fsw, as shown. In this example, output signal p(t) is at an amplitude of +1 responsive to input signal x(t) being instantaneously higher than the current state of the triangle waveform, and at an amplitude of −1 responsive to input signal x(t) instantaneously being lower than the current state of the triangle waveform. In this unity gain example, if input signal x(t) is at a DC level k, the mean value of PWM output signal p(t) over time is also at a level k.
In this conventional natural sampling PWM modulator 1 for AC input signals x(t) at an input frequency Fin, the modulation is theoretically perfectly linear, in the sense that no harmonic distortion is produced by comparator 5. However, non-harmonic components are produced, at side bands defined by the signal input frequency Fin, corresponding to multiples of the switching carrier frequency Fsw:N·Fsw±M·Fin  (1)These non-harmonic components are minimized if the switching (i.e., carrier) frequency Fsw is significantly higher than the input frequency of interest Fin. In audio applications, this situation is typically present.
In practice, however, non-idealities in the observed electrical performance of conventional natural sampling PWM modulator 1 indicate deviations from theoretical behavior, especially from the downstream switching power stage that is controlled by PWM output signal p(t). For example, noise and distortion arises from switching delays in the downstream power stage that vary non-linearly with load current. In the modulator itself, errors such as amplitude distortion and noise in the triangle wave signal will be evident as distortion and noise in the PWM output signal p(t). Comparator 5 may itself also contribute to distortion and noise. In addition, noise, ripple, and variations in the power supply voltage biasing the downstream switching stage will also introduce errors in the ultimate output.
According to conventional approaches, feedback control compensates for many of these non-ideal effects. FIG. 2 illustrates a conventional arrangement for a feedback-controlled PWM modulator 1. In FIG. 2, output power stage 7 is shown, as receiving PWM output signal p(t) and driving the ultimate output signal y(t) for driving audio speakers or the like. In this example, input signal x(t) to modulator 1 is derived from ultimate input signal i(t) combined with a feedback signal from output signal y(t). Output signal y(t) is subtracted from input signal i(t) by the operation of inverter 9 and adder 11. The difference signal from adder 11 is applied to loop filter 13, which produces modulator input signal x(t) after application of transfer function H(s). Transfer function H(s) determines both the stability of the system, and the extent to which error is suppressed by the feedback loop.
The system of FIG. 2 can be analyzed by considering it as a linear system with an additional input d(t) that represents the system error from all causes. This model is illustrated in FIG. 3, in which modulator 1 and power stage 7 are represented by linear gain stage 17. Adder 15 applies modeled error input d(t) to the output of gain stage 17. In the case of FIG. 2, in which the triangle wave amplitude and the power supply voltage are both unity, gain K is also unity (assuming a constant power supply voltage). One can characterize the error transfer function ETF(s) as follows:                               ETF          ⁡                      (            s            )                          =                  1                      1            +                          K              ·                              H                ⁡                                  (                  s                  )                                                                                        (        2        )            where K is the gain applied by gain stage 17. This error transfer function ETF(s) is the transfer function of error signal d(t) as it affects output signal p(t). The stability of the overall system can be determined from the poles of error transfer function ETF(s), and as such this stability depends on the gain K (which depends upon the power supply voltage) and on the transfer function H(s) of loop filter 13. Error suppression can be maximized by maximizing the gain of the loop filter 13 at the frequencies of interest; as evident from equation (2), the error suppression (i.e., the reciprocal of error transfer function ETF(s)) is effectively the loop filter gain itself, when this gain is sufficiently high.
The signal transfer function STF(s):                               STF          ⁡                      (            s            )                          =                              K            ·                          H              ⁡                              (                s                )                                                          1            +                          K              ·                              H                ⁡                                  (                  s                  )                                                                                        (        3        )            is substantially at unity gain in the band of interest (i.e., the frequencies at which the gain of loop filter 13 is high).
For the sake of this discussion, the system can be normalized so that gain K is unity, for example by normalizing the transfer function H(s) of loop filter 13 with the gain of modulator 1 and power stage 7, and by including any scaling in the feedback path. In effect, all gains outside of loop filter 13 can be considered as moved into, and thus compensated by, transfer function H(s). As typical in the art, the description in this specification will assume such normalization for clarity of description, although it is to be understood that gain values outside of the loop could be at values other than unity if desired.
Another non-ideal factor that affects the fidelity of class D amplifiers is ripple in the output signal p(t). More specifically, stability is optimized by the switching frequency of the PWM output signal being equal to the switching frequency Fsw of the triangular waveform. This characteristic is ensured by limiting the slew rate of the output of loop filter 13 to no more than the slew rate of the triangular waveform, which prevents the race-around condition in which the output of comparator 5 oscillates multiple times within a single period of the triangular waveform; this slew rate limitation holds true so long as waveform generator 3 in modulator 1 generates a substantially perfect triangle wave. These conditions also place an additional constraint on the transfer function H(s) of loop filter 13. It can readily be derived that ripple stability is attained by constraining the amplitude gain of transfer function H(s) at switching frequency Fsw:                                                     H            ⁡                          (                              F                sw                            )                                                ≤                  1          π                                    (        4        )            Conventional loop filters 13 typically have a slope of around 20 dB/decade at and just below the switching frequency, in order to ensure loop stability (i.e., placing closed loop poles in the left-hand plane). This constrains the unity gain frequency Funity to:                               F          unity                ≤                              F            sw                    π                                    (        5        )            
FIG. 4 illustrates a typical log-log response plot for a conventional loop filter in a natural sampling PWM modulator such as that in FIG. 2. At lower frequencies, the response slope is second-order, so that the error suppression carried out by the loop is maximized, while at higher frequencies, there are one or more zeros that reduces the slope to first order. In this regard, the unity gain frequency Funity is less than the switching frequency Fsw ensuring ripple stability as described above. FIG. 4 also illustrates that the maximum loop gain (i.e., the error suppression) at frequency Faudio (the upper limit of the audio band) is a function of the ratio of switching frequency Fsw to audio frequency Faudio. In general, a loop filter may have a magnitude characteristic over frequency with slopes that are higher than second-order, provided that there are zeroes that reduce the slope to near first-order (6 dB/octave) around the unity gain frequency Funity. These higher order loop filters will provide higher error suppression in the audio band.
Another concern faced by the designer of a PWM loop for audio amplification is the error due to aliasing in the feedback loop. As evident from this description, two PWM transitions occur in each switching period T, so that the sampling frequency is 2Fsw. If the input signal x(t) has frequency components above the Nyquist frequency (Fsw), aliasing will be present in the output. More specifically, those components in input signal x(t) that are at frequencies near the switching frequency Fsw will appear into the lower frequency audio band. This aliasing is, of course, undesirable for audio fidelity.
Referring back to FIG. 2, it is seen that high frequency components of the PWM output signal p(t) will feed back to the input of comparator 5. These high components are referred to as the ripple signal, which will produce an aliasing error when sampled by the comparator. In addition, because PWM output signal p(t) will have multiple side bands for each harmonic of switching frequency Fsw, these side bands will also alias down as harmonic distortion.
By way of further background, Berkhout, “Integrated Class D Amplifier”, presented at the 112th Conventional of the Audio Engineering Society (May 10–13, 2002; Munich), describes a class D amplifier that includes a second-order loop filter 13. The transfer function H(s) for this conventional filter is a weighted sum of a first order integrator and a second order integrator:                               H          ⁡                      (            s            )                          =                                                            K                1                            s                        +                                          K                2                                            s                2                                              =                                                                      K                  1                                ⁢                s                            +                              K                2                                                    s              2                                                          (        6        )            The first order integrator is a typical loop filter transfer function for simple class D amplifiers, as it has a zero real part for all positive integer multiples of the switching frequency Fsw, and thus produces no aliasing DC error. As known in the art, the second order integrator increases the error suppression in the base-band. The summed first and second order terms in the Berkhout loop filter introduces a real zero at s=−K2/K1 that reduces the phase characteristic to 90° for loop stability. However, it has been observed that the error function of the loop will be effectively set by the second-order integrator, and the error will scale with K2. The error suppression in the base-band also scales with K2, in which case the closed loop error will effectively be constant, such that increasing the second-order feedback by scaling K2 will be ineffective in decreasing distortion.